Red
Red is a Big Deal in Shyamalan's movies. The accepted reason is that he uses the color to draw attention to important items and people, and that definitely seems to be true here.
We'd argue that it goes beyond that function, though. In The Sixth Sense, you'll notice that red is visible at the point where the real world and the supernatural world collide. It's like a signal or a hint that something (or someone) otherworldly is about to come around. In Shyamalan's words, it alerts us to "anything in the real world that has been tainted by the other world" (source).
Take, for example, the red doorknob that goes down to Malcolm's basement. First of all, that's a really unusual color for a doorknob, so we really take notice of it (and it helps that Shyamalan always puts it in a close-up).
Plus, Malcolm has trouble opening that door for the entire movie—which seems weird until we find out that he's a ghost who, as such, has trouble manipulating real-world objects. Oh, and Malcolm's wife wears red for most of the film, too.
We don't see Cole's mother wearing red for most of the film. She's completely disconnected from his supernatural experiences. It's not until the scene in the car, when Cole fesses up, that she's wearing a red sweater; that's her initiation into knowledge of Cole's spirit world.
And then there's Cole's big red tent, which is his sanctuary from the ghosts that surround him. And how about Cole's red sweater and the red balloon at Darren's birthday party that leads Cole upstairs? Ditto Kyra's mother, with her red dress at the otherwise somber wake and her bright red lipstick. (We also see a bunch of red get-well cards for Kyra on the mantel in that scene.)
Why red? Does it represent blood, passion, just a shocking color?
Shmoop doesn't know, but it would make a good paper topic. Just sayin'.